In theory all the major browsers support SVG including support for SVG declarative animation. The quality of that support is variable and bugs come and go. In consequence, any statements made here may not be true tomorrow. The statements below refer to declarative animation in SVG
A major problem with some browsers is that they provide style sheet support as though it was defined for the complete HTML document so that if you have several SVG diagrams in a single HTML page, it is necessary to make sure each SVG style sheet is used just for that SVG diagram only. Adding an identifier to the initial SVG element and making all the stylesheet commands defined for that identifier will solve the problem. For example:
<svg id="f01" xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
width="640" height="500" >
<style type="text/css">
#f01 text.box {fill:black;stroke:none}
</style>
etc